Q.Assume that you would like to put money in an account today to make sure you have enough money in 10 years to buy a car. If you would like to have ₹10,000 in 10 years and you know you can get 5% interest per year from a savings account during that time, how much should you put in the account now?

Present Value, Future Value, and Net Present Value

The Core Intuition: Money Has a Time Address

A rupee today is not the same as a rupee a year from now. This isn't about inflation or risk yet — it's about opportunity. If you have ₹100 today, you can invest it. Even a simple bank deposit will turn that ₹100 into, say, ₹105 next year. So ₹100 today is equivalent to ₹105 one year later, given a 5% return.

This single idea is the foundation of all three concepts. Money has a time address — you cannot compare two amounts unless you first bring them to the same point in time.

Future Value (FV): What Will My Money Become?

Intuition: You put some money in a savings account or an investment. How much will it grow to after a certain number of years?

Precise statement: Future Value is the value of a current asset at a specified date in the future, based on an assumed rate of growth (the interest rate or rate of return).

The formula (simple annual compounding):

Where:

• $PV$ = Present Value (the amount you start with)
• $r$ = interest rate per period (as a decimal, e.g., 5% = 0.05)
• $n$ = number of periods (usually years)

Example: You deposit ₹10,000 at 8% per year for 3 years.

Your ₹10,000 grows to ₹12,597. The extra ₹2,597 is the time value of that money.

Present Value (PV): What Is a Future Amount Worth Today?

Intuition: Someone promises to give you ₹10,000 exactly three years from now. How much is that promise worth today? You cannot spend it now, and you lose the opportunity to invest your own money for those three years. So the promise is worth less than ₹10,000 today.

Precise statement: Present Value is the current worth of a future sum of money, given a specified rate of return (the discount rate). It is the reverse of Future Value — we discount the future amount back to today.

The formula:

Example: What is the present value of ₹10,000 to be received in 3 years, if the discount rate is 8%?

So ₹10,000 three years from now is worth only ₹7,938 today. The difference (₹2,062) is the discount — the cost of waiting.

Net Present Value (NPV): Is This Project Worth It?

Intuition: You are considering a business idea or an investment. It costs some money today (an outflow), and it will give you money later (inflows). Is it a good deal? You cannot just add up the inflows because they arrive at different times. You must bring everything — costs and benefits — to the same point in time (today), and then compare.

Precise statement: Net Present Value is the sum of the present values of all cash flows (both incoming and outgoing) associated with a project or investment, discounted at a given rate.

The formula:

Where:

• $C_t$ = net cash flow at time $t$ (positive for inflows, negative for outflows)
• $r$ = discount rate (the required rate of return)
• $t$ = time period (usually years; $t=0$ is today)

Decision rule:

• If $NPV > 0$: The project is profitable. It adds value beyond the required return.
• If $NPV < 0$: The project destroys value. Reject it.
• If $NPV = 0$: The project breaks even — it earns exactly the required return.

Example: A project costs ₹50,000 today. It will give ₹20,000 at the end of Year 1, ₹25,000 at the end of Year 2, and ₹30,000 at the end of Year 3. The required return is 10%.

Since ₹11,381 > 0, the project is worthwhile.

The Big Picture: How They Connect

• Future Value answers: "If I invest X today, what will I have later?"
• Present Value answers: "If I will receive X later, what is it worth today?"
• Net Present Value answers: "If I have a stream of costs and benefits over time, is the overall deal good or bad?"

All three rest on the same bedrock: a rupee today is worth more than a rupee tomorrow, because today's rupee can be put to work. The discount rate $r$ is the price of time — it captures the return you could earn elsewhere.